Manuals/calci/WEIBULL

WEIBULL(x,alpha,beta,lv)

$x$ is the value of the function.
$alpha$ and $beta$ are the parameter of the distribution.
$lv$ is the logical value.

Description

This function gives the value of the weibull distribution with 2-parameters.
It is a continuous probability distribution.
Weibull distribution also called Rosin Rammler distribution.
It is used to model the lifetime of technical devices and is used to describe the particle size distribution of particles generated by grinding, milling and crushing operations.
This distribution is closely related to the lognormal distribution.
In WEIBULL(x,alpha,beta,lv),x is the value to evaluate the function.
alpha is the shape parameter of the distribution.beta is the scale parameter of the distribution.
lv is the logical value which determines the form of the distribution.
When lv is TRUE, this function gives the value of the cumulative distribution. When lv is FALSE, then this function gives the value of the probability density function.
When we are not omitting the value of lv, then it consider as FALSE.
Weibull distribution is of two type :3-parameter weibull distribution and 2-parameter weibull distribution.
This function gives the value of 2-parameter weibull distribution by setting the third parameter (location parameter) is zero.
Also if alpha<1,then the failure rate of the device decreases over time.
If alpha=1, then the failure rate of the device is constant over time.
If alpha>1, then the failure rate of the device increases over time.
The equation for cumulative distribution function is: Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double exponent: use braces to clarify"): {\displaystyle F(x,\alpha ,\beta )=1-e^{-({\frac {x}{\beta }})}^{\alpha }} .
The equation for probability density function is:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double exponent: use braces to clarify"): {\displaystyle f(x,\alpha ,\beta )={\frac {\alpha }{\beta ^{\alpha }}}.x^{\alpha -1}.e^{-({\frac {x}{\beta }})}^{\alpha }.}

When alpha =1, then this function gives the exponentail with λ=1/β.
This function gives the result as error when

   1. Any one of the argument is non-numeric.
   2. x is negative.
   3.alpha  or beta <math>\le 0.

WEIBULL(x,alpha,beta,lv), where , and , and .

WEIBULL(x ,a, b, cum)

Where 'x' Is the value at which to estimate the function, 'a'(Alpha) and 'b'(Beta) are the parameters to the distribution, and 'cum' determines the form of the function.

This function returns the Weibull distribution.